Net Charge

The problem statement, all variables and given/known data
Initially, sphere A has a charge of –10e and sphere B has a charge of +20e. The spheres are made of conducting material and are identical in size. If the spheres then touch, what is the resulting charge on sphere A? a) +10e, b) -10e, c) -5e, d) +5e

The attempt at a solution
Sphere B -> [itex]20e-\left(\frac{+20e-10e}{2}\right) = 20e - 5e = 15e[/itex]. So there is a loss of 5e in Sphere B. This would mean that the only -5e remains on Sphere B?

The Problem
However, the answer is +5e. Why is this? There is a loss of 5e in Sphere B. This would mean that the only -5e remains on Sphere B?

What actually happens is that 15 electrons will move from A to B in order to equalize the charge distribution, thus:
A goes from -10e - (-15e) = +5e;
B goes from +20e + (-15e) = +5e.

Oh I see. Thanks for the help. You've been very patient and helpful. It was encouraging.

The reason that I was getting confused is because in Fundamentals of Physics, Chapter 21, Question 4, you have to use average to find the charge left over in the positive charge. Why is that different?

Staff: Mentor

The reason that I was getting confused is because in Fundamentals of Physics, Chapter 21, Question 4, you have to use average to find the charge left over in the positive charge. Why is that different?

The figure below shows three pairs of identical spheres that are to be touched together and then seperated. The initial charge on them are indicated. Rank the pair according to (a) the magnitude of the charge transferred during touching and (b) the charge left on the positively charged sphere, greatest first.

Staff: Mentor

In all cases the average charge tells you what the final charge on each sphere will be. To find the change in charge, just subtract final - initial.

For case (1) in your last post, you start with +6e and -4e. So the final charge on each will be (+6e -4e)/2 = +1e. Thus the change in charge on left sphere will be: +1e - 6e = -5e (it gained 5 electrons); on the right sphere, it will be: +1e - (-4e) = 5e (it lost 5 electrons).

Make sense? (Since the question asks for the magnitude of the charge transferred, the answer would be 5e.)